Yes this question can be solved using simultaneous equations. I have attached my solution below. Please let me know if I am correct. If you remember the value of sin30 you can easily derive the value of sin and cos of the other values easily (45, 60, 90 etc). Nevertheless I included some interesting (but not needed) derivations of any trig values I used.
Hi @Apaul466,
Yes this question can be solved using simultaneous equations. I have attached my solution below. Please let me know if I am correct. If you remember the value of sin30 you can easily derive the value of sin and cos of the other values easily (45, 60, 90 etc). Nevertheless I included some interesting (but not needed) derivations of any trig values I used.